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Article
Bernoulli–Dunkl and Euler–Dunkl polynomials and their generalizations
Bernoulli–Dunkl and Euler–Dunkl polynomials are generalizations of the classical Bernoulli and Euler polynomials, using the Dunkl operator instead of the differential operator. In this paper, we study properti...
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Article
The spectrum of the right inverse of the Dunkl operator
From the Dunkl analogue of Gegenbauer’s expansion of the plane wave, we derive an explicit closed formula for the spectrum of a right inverse of the Dunkl operator. This is done by stating the problem in such ...
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Article
A transference theorem for hermite expansions
A transference theorem for multipliers of Hermite expansions is proved. The result allows to transfer weightedL 2(ℝ n ) estimates from lower to higher dimensions.